具有奇异非线性的分数阶拉普拉斯方程正解的存在性与唯一性
偏微分方程分析
2014-03-14 v1
摘要
本文证明了在具有零 Dirichlet 边界条件的光滑有界域中，具有奇异非线性的分数阶拉普拉斯方程正经典解的存在性和唯一性。通过上下解方法，我们推导出了近似问题正经典解的存在性。为了获得正则性，我们首先建立了分数阶拉普拉斯方程弱解的存在性。得益于 \cite{XY}，正则性可由弱解的有界性得出。
引用
@article{arxiv.1403.3149,
title = {Existence, Uniqueness of Positive Solution to a Fractional Laplacians with Singular Nonlinearity},
author = {Yanqin Fang},
journal= {arXiv preprint arXiv:1403.3149},
year = {2014}
}
备注
In this paper we deal with the fractional Laplacian with singular nonlinearity. We prove the existence and uniqueness of the solution to this kind of equations. Although the nonlinearity is singular, we obtain the regularity of the solution. In order to derive existence of solution, we employ the method of sub- and supersolutions